Enhanced group classification of Benjamin-Bona-Mahony-Burgers equations

TL;DR

This paper performs a comprehensive Lie symmetry analysis of the Benjamin-Bona-Mahony-Burgers equations with time-dependent coefficients, classifies their symmetries, and constructs some exact solutions.

Contribution

It provides a complete group classification of BBMB equations with time-dependent coefficients using the method of mapping between classes.

Findings

Derived Lie symmetries enable reduction to ordinary differential equations.

Complete classification of admissible transformations.

Constructed explicit exact solutions.

Abstract

A class of the Benjamin-Bona-Mahony-Burgers (BBMB) equations with time-dependent coefficients is investigated with the Lie symmetry point of view. The set of admissible transformations of the class is described exhaustively. The complete group classification is performed using the method of mapping between classes. The derived Lie symmetries are used to reduce BBMB equations to ordinary differential equations. Some exact solutions are constructed.